Spring 2017


Asymptotics in Sequence Comparison

Special Topics course offered in Spring 2017 by Christian Houdre.

Advanced Graph Theory

Selection of topics vary with each offering.

Introduction to Operator Theory

Theory of linear operators on Hilbert space; spectral theory of bounded and unbounded operators; applications

Stochastic Processes and Stochastic Calculus II

An introduction to the Ito stochastic calculus and stochastic differential equations through a development of continuous-time martingales and Markov processes. (2nd of two courses in sequence)

Probabilistic Methods in Combinatorics

Applications of probabilistic techniques in discrete mathematics, including classical ideas using expectation and variance as well as modern tools, such as martingale and correlation inequalities.


Fundamental combinatorial structures including hypergraphs, transversal sets, colorings, Sperner families, intersecting families, packings and coverings, perfect graphs, and Ramsey theory. Algebraic and topological methods, applications.

Statistical Techniques of Financial Data Analysis

Fundamentals of statistical inference are presented and developed for models used in the modern analysis of financial data. Techniques are motivated by examples and developed in the context of applications. Crosslisted with ISYE 6783.

Fixed Income Securities

Description, institutional features, and mathematical modeling of fixed income securities. Use of both deterministic and stochastic models. Crosslisted with ISYE 6769.

Algebraic Topology I

The fundamental group, covering spaces, core topics in homology and cohomology theory including CW complexes, universal coefficients, and Poincare duality.

Stochastic Processes II

Continuous time Markov chains. Uniformization, transient and limiting behavior. Brownian motion and martingales. Optional sampling and convergence. Modeling of inventories, finance, flows in manufacturing and computer networks. (Also listed as ISyE 6762)


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